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Let's solve the math problem from the image:

**Problem 14:**
A poster is 15 inches wide and 24 inches tall. A smaller version of the poster is created using a scale factor of \( \frac{2}{3} \). What is the area of the smaller poster?

### Step 1: Find the dimensions of the smaller poster.
To find the dimensions of the smaller poster, we multiply both the width and the height of the original poster by the scale factor \( \frac{2}{3} \).

- Original width: 15 inches
  \[
  15 \times \frac{2}{3} = 10 \text{ inches}
  \]

- Original height: 24 inches
  \[
  24 \times \frac{2}{3} = 16 \text{ inches}
  \]

Thus, the dimensions of the smaller poster are 10 inches by 16 inches.

### Step 2: Calculate the area of the smaller poster.
Now, to find the area, we multiply the width and height of the smaller poster:
\[
\text{Area} = 10 \times 16 = 160 \text{ square inches}
\]

### Final Answer:
The area of the smaller poster is **160 square inches**.

Would you like a more detailed explanation, or do you have any questions?

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Here are five related questions to expand your understanding:

1. If the scale factor were \( \frac{1}{2} \), what would the area of the smaller poster be?
2. What would the perimeter of the smaller poster be with a scale factor of \( \frac{2}{3} \)?
3. How would the area change if the scale factor was instead \( \frac{3}{4} \)?
4. Can you find the reduction in area as a percentage when scaling down from the original poster?
5. What is the ratio of the area of the smaller poster to the area of the original poster?

**Tip:** When using a scale factor, remember that dimensions change linearly, but areas change quadratically (e.g., the scale factor squared affects the area).

A poster is 15 inches wide by 24 inches tall. A smaller version of the same poster is created using a scale factor of 2/3. What is the area of the smaller poster?

Learn how to calculate the area of a smaller poster with dimensions scaled down using a scale factor of 2/3 from an original size of 15 inches wide and 24 inches tall. The final area of the smaller poster is 160 square inches. Suitable for students in Grades 6-8.

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